After returning from my trip, I want to share my experience for anybody else who finds themselves in the same position. I arrived at the Opera House around 18:00 and went to the Stehplatzkasse. There was no queue at that point. The standing room tickets for the best seats were sold out by that time, but tickets remained available for the balcony and gallery levels. I bought a ticket for the gallery, which is the highest level. I made it upstairs around 18:15 for the 18:30 curtain, and found a single space along the rail almost all the way off toward house left. From there, I could see about half the stage. While not a perfect situation, it was certainly worth EUR 2 and a few hours of my time.